Application Of Effective Medium Theory Research Articles

Thermoelectric properties and effective medium theory analysis on the (GeTe)1-x(InTe)x composites

We employed the p-type semiconductor InTe as an extrinsic phase mixing in the GeTe matrix for thermoelectric properties investigations on the (GeTe)1-x(InTe)x (x=0, 0.02, 0.04, 0.06, and 0.08) composites. We observed notable phenomena that a small amount of InTe has a significant influence on the thermoelectric properties as the primary host matrix in the (GeTe)1-x(InTe)x (x=0.02, 0.04, 0.06, and 0.08) composites. Even for small concentrations of InTe which possess lower thermal and electrical conductivities compared to those of GeTe, the thermoelectric properties of the (GeTe)1-x(InTe)x (x=0.02, 0.04, 0.06, and 0.08) composites are primarily influenced by the properties of InTe. We systematically elucidated the electrical conductivity of the (GeTe)1-x(InTe)x (x=0.02, 0.04, 0.06, and 0.08) composites through the application of effective medium theory (EMT). It is found that the effective media of the (GeTe)1-x(InTe)x (x=0.02, 0.04, 0.06, and 0.08) composites is an asymmetric medium insulator. The addition of InTe into GeTe reveals a significant decrease in total thermal conductivity due to reductions in both electronic and lattice thermal conductivity. Particularly, the decrease in lattice thermal conductivity was attributed to an increase in internal strain within the lattice induced by the addition of InTe. Consequently, the ZT values of the composite significantly increase across all temperature ranges. This study suggests that developing composites is an effective approach for enhancing thermoelectric performance, comparable to elemental doping, and demonstrates the ability to analyze the electrical properties of composite materials using EMT.

Elastic wave velocity of marine sediments with free gas: Insights from CT-acoustic observation and theoretical analysis

The existence of free gas in pores will significantly affect the elastic wave velocity and attenuation coefficient of aqueous sediments. However, because the gas content and distribution are difficult to be accurately obtained through experiments, it is difficult to accurately characterize the relationship between elastic wave velocity and gas content, which may lead to the evaluation error of gas saturation in sediments. In this study, we applied the combined detection technology of X-CT and ultrasonic detection to simultaneously obtain the volume proportion of each phase and acoustic velocity of the selected marine sediments, respectively. On the basis of experiments, the applicability of effective medium theory (EMT), Biot-Gassmann theory by Lee (BGTL) and simplified three-phase equation (STPE) is verified. Meanwhile, the bulk modulus of pore fluid (Kfl) is recalculated by integrating Wood's and Domenico's equations by introducing calibration constant J to adapt to different reservoir conditions. The results show that the elastic wave velocities predicted by BGTL and STPE are more accurate compared with other gas estimation models. When J = −0.8, the acoustic velocity of sedimentary medium predicted by BGTL is more consistent with the experimental data. In addition, we apply the model to the elastic wave velocity data from ODP 204 Hole 1245 and obtain the free gas saturation. The results provide a theoretical and practical application reference for accurately estimating the free gas saturation in marine sediments.

Hydraulic conductivity estimation by considering the existence of piles: A case study

Estimation of hydraulic parameters is a critical step during design of foundation dewatering works. When many piles are installed in an aquifer, estimation of the hydraulic conductivity should consider the blocking of groundwater seepage by the piles. Based on field observations during a dewatering project in Shanghai, hydraulic conductivities are back-calculated using a numerical model considering the actual position of each pile. However, it is difficult to apply the aforementioned model directly in field due to requirement to input each pile geometry into the model. To develop a simple numerical model and find the optimal hydraulic conductivity, three scenarios are examined, in which the soil mass containing the piles is considered to be a uniform porous media. In these three scenarios, different sub-regions with different hydraulic conductivities, based on either automatic inverted calculation, or on effective medium theory (EMT), are established. The results indicate that the error, in the case which determines the hydraulic conductivity based on EMT, is less than that determined in the automatic inversion case. With the application of EMT, only the hydraulic conductivity of the soil outside the pit should be inverted. The soil inside the pit with its piles is divided into sub-regions with different hydraulic conductivities, and the hydraulic conductivity is calculated according to the volume ratio of the piles. Thus, the use of EMT in numerical modelling makes it easier to consider the effect of piles installed in an aquifer.

Screening polyethylene oxide-based composite polymer electrolytes via combining effective medium theory and Halpin-Tsai model

Polyethylene oxide (PEO) based materials are promising candidates for the matrices in composite solid polymer electrolytes (CSPEs) for high-energy density lithium ion batteries. Experimental screening of high-performance CSPEs with high efficiency still appears to be challenging for the moment, due to the complications of the compositions involved. Here, we propose and test the joint application of effective medium theory (EMT) and Halpin-Tsai model that can predict with satisfactory accuracy the effects of the filler volume fractions and of the particle sizes on the conductivities and Young’s moduli of CSPEs. The application of this theoretical framework can be extended to other polymer based CSPEs and potentially enables us to build a CSPEs database for data mining to accelerate the screening process.

Applicability of Effective Medium Approximations to Modelling of Mesocrystal Optical Properties

Rigorous superposition T-matrix method is used to compute light interaction with mesocrystalline structures. The results are used to validate the applicability of effective medium theories for computing the effective optical constants of mesocrystal structures composed of optically isotropic materials. It is demonstrated that the Maxwell-Garnett theory can fit the rigorous simulation results with an average accuracy of 2%. The thus obtained refractive indexes can be used with any electromagnetic simulation software to represent the response of mesocrystals composed of optically small primary particles arranged into a cubic type lattice structures.

On the mapping of Dirac-like cone dispersion in dielectric photonic crystals to an effective zero-index medium

Two-dimensional (2D) dielectric photonic crystals with accidentally induced Dirac-like points (DLPs) at the Brillouin zone center behave as an effective zero-index medium under certain conditions. We investigated different 2D square lattice dielectric PCs, such as dielectric rods of square and circular cross sections and core–shell rods in a square lattice, and cataloged the conditions under which these PCs can mimic an effective zero-index medium. We found that PCs with DLPs formed by dipole and quadrupole moments cannot be mapped to an effective zero-index metamaterial (ZIM) even if the DLP is at low frequency, indicating the applicability of effective medium theory. The effective ZIM can only be realized in PCs with DLPs if all three of the following conditions are fulfilled simultaneously: (i) the DLP is formed by monopole and dipole moments, (ii) the DLP is at low enough frequency, and (iii) there is only one propagating band in the extended states above the DLP frequency. The shape of the iso-frequency contours does not play a significant role toward the mapping of the DLP to an effective ZIM.

Impacts of semi-transparent window on reflectance from metallic gratings at oblique incidence

This work both numerically and experimentally investigates the reflectance from the smooth side of a semi-transparent 508-µm-thick window with metallic gratings attached on the other side. The incident light is oblique and linearly polarized, and its wavelength ranges from 2.5 to 25 µm. Three gratings with various levels of profile complexity and periods are investigated. Influences from the intrinsic material absorption, light refraction, total internal reflection, interference, and diffraction on both the specular and hemispherical reflectance are studied. Moreover, the applicability of effective medium theory to our samples is verified.

Applicability of effective medium theory to wood density measurements using terahertz time-domain spectroscopy

The use of an effective medium theory is important when accurately measuring wood density using millimeter and terahertz wave techniques. To confirm the applicability of this theory to the evaluation of wood density, the relative permittivity and dielectric loss of oven-dry flat-sawn specimens of 11 different wood species were measured in a frequency range of 0.15–1.2 THz using a transmission measurement system for terahertz time-domain spectroscopy. A mixture model based on the effective medium theory well explained the density dependence of relative permittivity over the entire frequency range, while it did not fully explain that of dielectric loss, especially for higher frequencies. This indicates that wood scatters the terahertz wave with a wavelength close to the transverse sectional dimensions of the pores in wood in the same way as Mie scattering. It was found from the dielectric loss spectrum of wood substance that the frequency around 0.23 THz was preferable for the nondestructive evaluation of wood.

Application of effective medium theory with consideration of island shapes to interpret optical properties of discontinuous Pt films

Pt films with mass thicknesses ranging from 0.6 to 3.9 nm were evaporated onto quartz-glass substrates under vacuum conditions (p ~ 10(-4) Pa) with evaporation rate 0.01 to 0.2 mm/s. The transmittance spectra were measured in the wavelength range from 220 to 2500 nm. The microstructures were examined by a transmission electron microscope. The statistical distributions of island areas and the histograms of the fixed ratios of the semiaxes for ellipsoids were determined. It has been found that the transmittance spectra for the films with coverage coefficient 0.2≤p≤0.6 exhibit minima that shift with an increase in the coverage coefficient. To interpret the transmittance spectra of the films, the Maxwell-Garnett theory, which takes into account the island shapes, was used. Measured and calculated spectra were compared. For low coverage coefficients there is a quantitative agreement between the experimental and the calculated results.

The application of effective-medium theory for the nondestructive characterization of ceramic composites

In this paper is presented the application of effective-medium theory (EMT) on ferrite ceramic composites with various volume fractions of spinel phase in an M-hexaferrite matrix in order to determine the phase composition. The permeabilities, which were calculated with effective-medium theory from measured permeabilities of single-phase samples, were matched with measured effective permeability of composite samples. From analysis of composites sintered at two different temperatures it is also shown that by presented method one can detect the formation of new phases. In this way obtained volume fractions of spinel phase were compared with values from the X-ray powder diffraction (XRD) analysis and the nominal composition mass. It is shown that EMT quantitative phase determination of magnetic composites is comparable to XRD quantitative phase analysis and represents a simple and fast complementary alternative.

Electrical and elastic properties of new monolithic wood-based carbon materials

Carbonaceous monolithic materials were prepared from especially designed wood-based composites consisting of wood fibres and phenolic resin binder. By compressing more or less the starting materials, the monoliths were obtained with densities ranging from 0.3 to 1.2 g cm−3. After carbonisation, electrical conductivity and elastic moduli of a number of samples were investigated, and typical percolation behaviours were evidenced for both properties close to their respective critical points. Careful study of the apparent density and pore texture of the uncompacted carbonised fibres allowed the determination of the conductivity threshold Φc. The morphologies of both the constitutive carbon particles and the interparticle voids were derived from application of effective-medium theory; the calculated aspect ratio of the fibres was found to be in good agreement with both SEM characterisations and other calculations based on percolation theory. Observation of the universal 3D value of the critical conductivity exponent supported the accuracy of the estimated value of Φc. The rigidity threshold Φr was also determined, and the relevance of the Kirkwood-Keating model accounting for the observed relationship between Φc and Φr was established. The value of the elasticity critical exponent suggested central forces between the fibres, further supporting the suitability of the Kirkwood-Keating model. To the knowledge of the authors, such a model was shown to apply to only one other material so far: expanded graphite. Hence, the present work shows the relevance of the classical concepts of disordered matter physics for describing heterogeneous random carbonaceous materials.

Effective medium theories in surface enhanced infrared spectroscopy: The pentacene example

Effective medium theory (EMT) is a semiempirical approach developed to predict the response properties of composites. In particular, EMT has been applied to the study of rough metal surfaces that can enhance the absorption of electromagnetic radiation in the infrared [surface-enhanced infrared absorption (SEIRA) or in the visible (surface-enhanced visible]. The application of EMT provides a formalism to simulate the effective dielectric function of the inhomogeneous medium, for instance, of metal-organic thin films. The EMT is widely applied when the dimensions of the inhomogeneties (granular components in the mixed film) are smaller than the wavelength of the incident radiation. The computational approach to SEIRA using EMT, and the experimental SEIRA results for pentacene are presented here. First, enhancement factors are calculated using EMT method for pentacene on Ag, Cu, and Sn. Vibrational intensities for each symmetry species are obtained using DFT B3LYP at the 6-31G(d) level of theory. Second, from the set of experimental data provided by reflection- absorption infrared (RAIRS) and transmission FT-IR spectra of a 15 nm pentacene film evaporated onto reflecting and IR transparent support substrates, respectively, the molecular orientation and the interpretation of the observed spectra in conformity with the surface selection rules was extracted. The interpretation of the pentacene SEIRA spectra of a 15 nm pentacene film on silver and tin islands is presented and its compliance with surface selection rules is discussed.

Analysis of binary electrochromic tungsten oxides with effective medium theory

Multicomponent oxides are of increasing interest for electrochromic electrodes. To reduce the large number of permutations in composition it would be useful to be able to predict the properties of the mixtures from the pure oxide components. WO 3 mixed with V 2O 5 has been produced by a sol–gel technique in order to increase durability and color neutrality of conventional WO 3 electrochromic coatings. Chemical composition was confirmed by Rutherford backscattering spectrometry (RBS). Surface morphology was analyzed by atomic force microscopy (AFM). Electrochromic performance of the films was tested by cyclic voltammetry with in-situ transmission control. Optical constants of vanadium tungsten oxides were determined over the whole solar spectrum. The measurements included variable angle spectroscopic ellipsometry and spectral transmittance and reflectance. An attempt is made to treat doped tungsten oxide as an effective medium consisting of a mixture of WO 3 with V 2O 5. In the clear state, comparison of optical constants and thickness directly determined on the samples yields qualitative agreement with results from effective-medium analysis. The resulting component fraction also agrees as long as the film density does not deviate too much from the linearly interpolated value between the pure components. For the colored state, preferential trapping of electrons at one atom species hinders the application of effective medium theory.

Applicability of effective medium theory to ferroelectric/ferrimagnetic composites with composition and frequency-dependent complex permittivities and permeabilities

High-frequency (1 MHz–1 GHz) transmission line measurements were used to determine the composition and frequency-dependent complex permittivities and complex permeabilities of ferroelectric/ferrimagnetic (barium titanate and a magnesium-copper-zinc ferrite) composites. The effective medium rules of Maxwell–Garnett give both lower and upper bounds for the effective permittivities and permeabilities and yield accurate estimates of the bulk electric and magnetic properties at low volume fill fraction of either component provided the proper host matrix is chosen. Bruggeman theory yielded the best predictive values for the permittivity and permeability over the entire composition range. In all cases these complex quantities were shown to be constrained by Bergman–Milton bounds.

Effective medium theory in studies of conductivity of composite polymeric electrolytes

The application of effective medium theory to a description of a temperature and composition dependence of conductivity of composite polymeric electrolytes is presented. Conductivities of several composite systems containing conducting (NASICON) or nonconducting (Θ-Al 2O 3, polyacrylamide) additives are analyzed in terms of effective medium theory approaches. All of the systems studied are based on polyether matrices. The influence of grain size distribution, concentration and type of additives on conductivity of composite systems is discussed. The model presented assumes that an increase in the conductivity in comparison to polyether based electrolytes is due to the formation of highly conductive layers at the polyether matrix-filler interface. Variation of the conductivity of this layer with grain sizes, and the concentration of a filler is assumed and discussed. The theoretical assumptions are confirmed by experimental data obtained by several techniques, such as impedance spectroscopy, DSC, NMR and energy dispersive X-ray diffractometry.

Modeling of transport of small molecules in polymer blends: Application of effective medium theory

AbstractThis article concerns itself with the prediction of effective diffusion coefficients of small permeants in binary polymer blends of varying degrees of miscibility and microstructural order. Several models have been critically evaluated with the help of previously published experimental data and in terms of consistency of morphological information provided by small permeants serving as morphological probes. Completely random, two‐phase media have been modeled in terms of Effective Medium Theory with the coordination number (z) describing the average morphology. A comprehensive analysis of experimental data has shown a correlation between z and various physical situations. Near the percolation threshold, z attains a maximum value while, above it, z tends to decrease with increasing content of the conductive component. Accurate predictions of effective diffusivity can be made for volume fractions between 0.3 and 0.8 by letting z = 6. Evidence for phase inversion was studied in terms of models with ordered microstructure and transport data.

Application of effective-medium theory to inversion layers

Two-dimensional effective-medium theory is applied to the macroscopic-inhomogeneity model for transport in inversion layers near the threshold of conduction. The predicted behaviour resembles that which has been observed provided that reported Hall measurements have been made at carrier concentrations above the percolation threshold. The theory predicts a dramatic change in behaviour below the percolation threshold and extension of Hall measurements to lower carrier concentrations would provide an acid test of the validity of the model.